Formulae for converting to and from astronomy-relevant units
(meaning of abbreviations below)
1 candela/m2 :
= 0.0001 Stilb
= 0.3142 MilliLambert
= 0.2919 Footlambert
= 12.58 magnitudes/arcsec2
From candela/m2  magnitudes/arcsec2
B=-2.5Log(C/108000) or 12.58-2.5Log(C)
From magnitudes/arcsec2  candela/m2
C=108000*10-0.4B or 10(12.58-B)/2.5
1Lux :
= intensity of 1 candela on surface orthogonal to the light ray’s of the source,
at 1 meter distance from the source
= 1lumen/area (m2)
= 0.093 Footcandles
= -14.18 Stellar magnitudes*
From Lux  stellar magnitude
Mv = -14.18-2.5Log(L)
From stellar magnitude Lux
10(-14.18-Mv)/2.5
From footcandles stellar magnitudes
-16.8-2.5Log(Fc)
From stellar magnitudes footcandles
10(-16.8-Mv)/2.5
1 footLambert
= 11.25 magnitudes/arcsec2
From footLambert magnitudes/arcsec2
Mv=11.25-2.5Log(F)
From magnitudes/arcsec2 footLambert
10(11.25-Mv)/2.5
Formulae derived from Schaefer 1989, formulae 2,16, 17
From millimicroLambert (nanoLambert)  magnitudes/arcsec2
B = 26.33-2.5Log(M)
From magnitudes/arcsec2 millimicroLambert (nanoLambert)
M = 10-0.4(B-26.33)
Limiting vis. magnitude for background brightness in magnitudes/arcsec2 ≤ 18.4 (= photopic)
Mv = 4.11-5Log(1+102.316-B/5)
Background Brightness in magnitudes/arcsec2 photopic vision (for Mv ≤ 4.00)
B = 11.58-5Log(100.822-Mv/5-1)
Background Brightness in magnitudes/arcsec2 for scotopic vision (derived by Nils Olof
Carlin, see http://w1.411.telia.com/~u41105032/visual/Schaefer.htm) and adapted by myself
for a maximum darkness of 22 magnitudes/arcsec2
B=22-5Log(101.7-Mv/5-1)
Limiting vis. magnitude for background brightness in magnitudes/arcsec2for scotopic vision
(idem, Nils Olof Carlin)
Mv=8.5-5Log(1+104.4-B/5)
-----------------------------------------------B = Background brightness (BB) in magnitudes/arcsec2
M = BB in nanoLambert
Mv = visual limiting magnitude
C = candela’s
L = Lux
F = footLambert
Fc = footcandle
Log has base 10
* -14.18 = magnitude of 1 Lux. Other values: -14.04 or -13.89 (see Martynov, 1959; De
Vaucouleurs, 1964)
(Jan van Gastel, May 2009)
Comments are welcome